In this paper, the physical spline finite element method (PSFEM) is applied to the fullwave analysis of inhomogeneous waveguides. Combining (rectangular) edge element and the PSFEM, the cubic spline interpolation is successfully applied to the wave equation. For waveguide problems, the resulting nonlinear eigenvalue problem is solved by a simple iteration method in which the initial estimate is taken as the linear Lagrange interpolation, and then the solutions are improved by a few iterations. The bandwidth of the resultant matrix from the PSFEM is the same as that of linear Lagrange interpolation and is sparse. As a result, sparse matrix solver can be used. Three typical examples are demonstrated and compared with the analytical solutions and with the linear Lagrange interpolation results. It is observed that the present method converges much faster than the Lagrange interpolation method.
"Application of Physical Spline Finite Element Method (PSFEM) to Fullwave Analysis of Waveguides," ,
Vol. 60, 19-41, 2006. doi:10.2528/PIER05081102
1. Silvester, P., "Finite-element solution of homogeneous waveguide problems," Alta Frequenza, Vol. 38, 313-317, 1969.
2. Silvester, P. P. and G. Pelosi, "Finite Elements for Wave Electromagnetics: Method and Techniques," IEEE Press, 1994.
3. Jin, J., "The Finite Element Method in Electromagnetics," John Wiley & Sons, 1993.
4. Paulsen, K. D. and D. R. Lynch, "Elimination of vector parasites in finite element Maxwell solutions," IEEE Trans. Microwave Theoryand Tech., Vol. 39, 395-404, 1991. doi:10.1109/22.75280
5. Webb, J. P. and B. Forghani, "Hierarchal scalar and vector tetrahedra," IEEE Trans. on Magnetics, Vol. 29, 1495-1498, 1993. doi:10.1109/20.250686
6. Liang, X., B. Jian, and G. Ni, "The B-spline finite element method in electromagnetic field numerical analysis," IEEE Trans. on Magnetics, Vol. MAG-23, 2641-2643, 1987. doi:10.1109/TMAG.1987.1065516
7. Mitchell, A. R., "Variational principles and the finite element method," J. Inst. Maths. Applic., Vol. 9, 378-389, 1972.
8. Zhou, X., "Physical spline finite element (PSFEM) solutions to one dimensional electromagnetic problems (abstract)," J. of Electromagn. Waves and Appl., Vol. 17, No. 8, 1159-1160, 2003. doi:10.1163/156939303322519784
9. Zhou, X., "Physical spline finite element (PSFEM) solutions to one dimensional electromagnetic problems," Progress in Electromagnetics Research, Vol. 40, 271-294, 2003.
10. Zhou, X. and G. Pan, "Application of physical spline FEM to waveguide problems," PIERS 2000 Progress in Electromagnetics Research Symposium, 2002.
11. Pan, G. and J. Tan, "General edge element approach to lossy and dispersive structures in anisotropic media," IEE Proc. - Microw. Antennas Propag., Vol. 144, 81-90, 1997. doi:10.1049/ip-map:19970507
12. Collin, R. E., "Field Theoryof Guided Waves," IEEE Press, 1991.
13. Jackson, J. D., Classical Electrodynamics, John Wiley & Sons, New York, 1975.
14. Crowley, C. W., P. P. Silvester, and H. Hurwitz, "Covariant projection elements for 3D vector field problems," IEEE Trans. Magnetics, Vol. 24, 397-400, 1988. doi:10.1109/20.43940
15. Silvester, P. P., Finite Elements for Electrical Engineers, Cambridge University Press, New York, 1990.
22. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, New York, 1989.
23. Lu, Y. and A. Fernandez, "An efficient finite element solution of inhomogeneous anisotropic and lossy dielectric waveguides," IEEE Trans. Microwave Theoryand Tech., Vol. 41, 1215-1223, 1995. doi:10.1109/22.238548
24. Pincherle, L., "Electromagnetic waves in metal tubes filled longitudinally with two dielectrics," Physical Review, Vol. 66, 118-130, 1944. doi:10.1103/PhysRev.66.118
25. Harrington, R. F., "Time-Harmonic Electromagnetic Fields," McGraw-Hill, 1961.
26. Hano, M., "Finite-element analysis of dielectric-loaded waveguides," IEEE Trans. Microwave Theory Tech., Vol. MTT-32, 1275-1279, 1984. doi:10.1109/TMTT.1984.1132837
27. Koshiba, M., K. Hayata, and M. Suzuki, "Finite-element formulation in terms of the electric-field vector for electromagnetic waveguide problems," IEEE Trans. Microwave Theory Tech., Vol. MTT-33, 900-905, 1985. doi:10.1109/TMTT.1985.1133148
28. Bardi, I. and O. Biro, "Improved finite element formulation for dielectric loaded waveguides," IEEE Trans. on Magnetics, Vol. 26, 448-453, 1990. doi:10.1109/20.106350
29. Marcuvitz, N., Waveguide Handbook, Peter Peregrinus Ltd, New York, 1985.